Durmaz, born in Sweden to Assyrian parents who emigrated from Turkey, attempted to play down the abuse that had appeared on his Instagram account after the 2-1 defeat in Sochi.
"It's nothing I'm bothered about," the Toulouse player told reporters. "I'm here proud and representing my country."
Durmaz's teammates condemned the abuse, striker John Guidetti telling Aftonbladet: "He ran and fought the entire time. It's bad luck. It's completely idiotic to give him hatred because of it."
Sweden remain in the hunt for a last-16 place and next face Mexico in Yekaterinburg on Wednesday.